The propose research will address a great challenge of modern human genetics which is to understand the recent evolutionary history of our species. This is important not only as key basic knowledge, but also for many medical genetic questions, such as when and where have mutations occurred that contribute to diseases. The backdrop for medical questions like these is the demographic history of human populations, which includes our history of population sizes, population founding events, migrations and admixture, and population size changes. Two new methods for estimating the demographic history of a species will be developed. Both of these have been designed to address three major challenges that limit current methods. First, methods that are intended to study the history of gene exchange must include recombination as part of the model because of the strong interaction affect that recombination and gene exchange have on patterns of genetic variation. Second, methods must be able to handle large, complex demographic models with human populations. This is especially true for histories with gene exchange. Third, methods must be able to handle very large data sets with speed and without introducing biases. One new method will provide estimates of the Allele Frequency Spectrum (AFS) for pairs of linked single-nucleotide- polymorphisms (SNPs). By including recombination for pairs of SNPs, the 2 SNP AFS is far larger and holds much more information on gene exchange than the conventional single SNP-based AFS. The second new method will be a new genealogy sampling approach that uses a greatly reduced representation of genealogies (gene trees). This method does not give up any information, and yet unlike most current genealogy samplers will be able to be used for models with recombination and for large data sets. The third goal is to apply these methods to the study of human demographic history among African populations. African populations have ancient and complex genetic histories that include all of the major demographic processes considered here. Both methods will be applied to a large high-quality population genomic data set that currently includes 33 genomes from 7 populations, including three hunter-gatherer populations. The goal is an accurate and rich multi- population portrait of human history in Africa.